Quote from: cdnbcguy on September 23, 2013, 03:58:02 AM

I've done the math.

What we have here is a Bernoulli distribution - only ones and zeros but it still has a mean and a variance.

The variance in such a distribution is the probability of an event happening times one minus the probability of that event happening divided by the number of times it has an opportunity to happen.

The probability of us, the investors, winning any one bet is 51 % so the variance is 0.51 * 0.49 or 0.2499 divided by the number of bets.

A Bernoulli distribution always describes a bell curve. The greater the variance the fatter the bell curve, but this one always peaks at 0.51.

Our profit is all the curve that is on the right side of 0.5 (the mean of a fair coin toss) and our loss is all the curve on the left side of 0.5.

What we WANT is a curve with no variance at all. A straight line. We take the bet, shave off 1 percent and give the 99 % back. They give it back to us and we shave 1 percent again and give it back etc etc. Every 72 times this happens, we are keeping half the original stake.

But in real life there is variance. We don't get a straight line, we get a bell curve.

You will notice that with 51 % probability of winning we are intrinsically slightly advantaged. That's the whole point.

When the whale makes one huge bet of amount N the variance on the one bet is 0.2499 and the standard deviation of that is the square root of the variance which is 0.4999. That is a big fat curve of mean 0.51 and standard deviation of 0.4999. The amount of the curve to the left of 0.5 (the one where we the investors lose the bet) is 49.2 % - the part were we win is 50.8 %.

That is NUTS. We're betting a huge amount on a coin toss. The chance we make a profit (the portion of the curve to the right of 0.5) is only about 51%.

Oh, but that's an advantage you say! Look - if we take that bet we are gamblers and the whole point of investing is to not be a gambler. I'm not betting a wad of Bitcoins on a coin toss.

Besides - watch this! I'll show you what a REAL advantage looks like!

Let's get the same N bet in 1,000 small bets of N / 1,000.

Suddenly the variance is 0.2499 / 1,000 -> 0.0002499 - and the standard deviation is 0.0158

The curve this time is still peaking at 0.51 but it is much narrower. It is much closer to that ideal line we want. The area to the left of 0.5 - the losing bets - is about 24 % of the curve. To the right - 76 %.

We profit 76 % of the time over 1,000 bets - not 50.8 % of the time like with 1 bet.

THAT'S being an investor, not a gambler.

Also - has anyone noticed that despite the 1 percent edge JD has never made a 1 % profit? It was about half that - before the current fiasco - now we know why.

Variance. Lets lower it by refusing big bets.

This has been mentioned to Dooglus many times, his answer he always gives if you want less exposure then decrease your investment. There will be no change. Either accept the conditions or divest.